Every Odd Perfect Number Has a Prime Factor Which Exceeds
نویسنده
چکیده
It is proved here that every odd perfect number is divisible by a prime greater than 106.
منابع مشابه
Every odd perfect number has a prime factor which exceeds 106
It is proved here that every odd perfect number is divisible by a prime greater than 106.
متن کاملOn the Largest Prime Divisor of an Odd Perfect Number . II
It is proved here that every odd perfect number has a prime factor greater
متن کاملThe third largest prime divisor of an odd perfect number exceeds one hundred
Let σ(n) denote the sum of positive divisors of the natural number n. Such a number is said to be perfect if σ(n) = 2n. It is well known that a number is even and perfect if and only if it has the form 2p−1(2p − 1) where 2p − 1 is prime. It is unknown whether or not odd perfect numbers exist, although many conditions necessary for their existence have been found. For example, Cohen and Hagis ha...
متن کاملOdd perfect numbers have a prime factor exceeding 108
Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding 107. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding 108.
متن کاملOdd Perfect Numbers Have a Prime Factor Exceeding
It is proved that every odd perfect number is divisible by a prime greater than 107.
متن کامل